Question

A small bubble rises from the bottom of a lake where the temperature and pressure are 4.0 c and 3.0 atm, to the water’s surface, where the temperature is 25 c and the pressure is 0.95 atm. calculate the final volume of the bubble if the initial volume was 2.1 ml. a) 0.72 ml b) 6.2 ml c) 7.1 ml d) 22.4 ml e) 41.4 ml

Answer 1

The final volume of the air bubble when it reaches the surface of the lake is calculated to be 7.1 mL using the combined gas law. This results from temperature and pressure changes the bubble undergoes as it rises to the surface.

Step-by-step explanation:

To find the final volume of a gas bubble that rises from the bottom to the surface of a lake, we need to use the combined gas law, which is given by the equation:

P1V1/T1 = P2V2/T2, where P is the pressure, V is the volume, and T is the temperature in Kelvin.

Firstly, convert temperatures from Celsius to Kelvin by adding 273.15:

• T1 = 4.0 °C + 273.15 = 277.15 K
• T2 = 25.0 °C + 273.15 = 298.15 K

Now, we can rearrange the combined gas law to solve for the final volume V2:

V2 = P1V1T2 / (P2T1)

Plugging in the values:

• P1 = 3.0 atm
• V1 = 2.1 mL
• P2 = 0.95 atm
• T1 = 277.15 K
• T2 = 298.15 K

V2 = (3.0 atm × 2.1 mL × 298.15 K) / (0.95 atm × 277.15 K)

V2 = (1881.45 mL·K) / (263.2925 atm·K) = 7.14 mL

The final volume of the bubble when it reaches the surface of the lake is approximately 7.1 mL, which corresponds to choice (c).